Technical Field
This disclosure relates generally to oil and gas well logging, and more specifically, to directional resistivity measurements. Still more specifically, two embodiments of a method are disclosed for determining resistivity anisotropy and formation structure from deep resistivity measurements in vertical wellbore sections. Other measurements are disclosed as well.
Description of the Related Art
An alternative to wireline logging techniques is the collection of data on downhole conditions during the drilling process. By collecting and processing such information during the drilling process, the driller can modify or correct key steps of the operation to optimize performance. Schemes for collecting data of downhole conditions and movement of the drilling assembly during the drilling operation are known as measurement-while-drilling (“MWD”). Similar techniques focusing more on measurement of formation parameters than on movement of the drilling assembly are known as logging-while-drilling (“LWD”). However, the terms MWD and LWD are often used interchangeably, and the use of either term in this disclosure will be understood to include both the collection of formation and wellbore information, as well as data on movement and placement of the drilling assembly.
Measurement-while-drilling (MWD) tools are available to guide drill strings and therefore the resulting wellbores into more productive reservoir zones. MWD tools used for this purpose typically have been propagation resistivity tools, also known as array compensated resistivity (ARC) tools, with a 360° measurement and deep imaging capability to detect fluid contacts and formation changes up to 15 feet from the wellbore. Measurements are commonly made of the phase-shift and attenuation of the signals at the receiver coils, which are indicative of the formation conductivity.
Currently available ARC tools are non-azimuthal and use two receivers to compensate for any electronic drift associated with the transmitter. The electronic drift associated with the two receivers and any imbalance between the two receivers is removed using a scheme called borehole compensation, which involves the use of a second transmitter symmetrically placed with respect to the first transmitter. The transmitters are alternately energized so two phase shifted signals can be measured when the two transmitter coils operate at identical frequencies. However, using two transmitter coils alternately slows the rate of data acquisition, which can lead to errors due to the time delay between sequential measurements. Further, use of multiple transmitters may require the signals to be time-multiplexed when operating at the same frequency to avoid cross-talk. Multiplexing slows the rate of data acquisition. The errors due to time delays are magnified when drilling rates are high.
Another problem associated with conventional propagation resistivity or ARC tools is that the magnetic dipole moments of the transmitters and receivers are oriented axially with respect to the tool axis. Such measurements are only sensitive to or affected by the anisotropy when the relative dip angle (θ) is greater than 45° . Further, in homogeneous formations, vertical resistivity and relative dip angle are coupled. As a result, even with a relative high dip angle, simultaneous determination of horizontal resistivity (Rh), vertical resistivity (Rv), and the relative dip angle (θ) is not possible for homogeneous formations. Environmental effects may break the coupling between Rh and θ, but that is uncertain and variable from formation to formation.
As an improvement over propagation resistivity or ARC tools, Schlumberger developed the PERISCOPE™ 15 deep imaging LWD tool, which incorporates tilted and transverse antennas in the drilling collar. The non-axial antennae obtain directional electromagnetic measurements. One can define the attenuation ATT as a logarithmic function of the ratio between two different linear combinations of the electromagnetic coupling tensor coefficients Vxx, Vyy, and Vzx:
                    ATT        =                  20          ⁢                                    log              10                        ⁡                          (                              abs                ⁡                                  (                                                                                    V                        xx                                            +                                              V                        yy                                            +                                              V                        xz                                                                                                            V                        xx                                            +                                              V                        yy                                            -                                              V                        xz                                                                              )                                            )                                                          (                  1          ⁢          a                )            and the phase shift PS as the difference between two arctangent functions, using real and imaginary components of the electromagnetic coupling tensor components, at the same wellbore station:
                    PS        =                              a            ⁢                                                  ⁢                          tan              ⁡                              (                                                                            V                      xx                      i                                        +                                          V                      yy                      i                                        -                                          V                      xz                      i                                                                                                  V                      xx                      r                                        +                                          V                      yy                      r                                        -                                          V                      xz                      r                                                                      )                                              -                      a            ⁢                                                  ⁢                                          tan                ⁡                                  (                                                                                    V                        xx                        i                                            +                                              V                        yy                        i                                            +                                              V                        xz                        i                                                                                                            V                        xx                        r                                            +                                              V                        yy                        r                                            +                                              V                        xz                        r                                                                              )                                            .                                                          (                  1          ⁢          b                )            
These directional measurements, for which the electronic drifts of both the transmitter and receiver are removed (or gain corrected), are used to determine the distance to and azimuthal orientation of formation boundaries in any type of mud. These measurements are typically transmitted uphole and displayed on a graphical interface to provide information on distance to boundaries, formation resistivity, and orientation. These measurements are sensitive to resistivity anisotropy even at very low relative angles (e.g., 10°), which is critical in low resistivity pay zones and in laminated formations because accurate identification and characterization of hydrocarbon reserves is not possible without knowing the resistivity anisotropy.
Unfortunately, the azimuthal sensitivity of a non-axial transmitter/receiver pair disappears in a perfectly vertical section with 0° relative dip angle θ. In other words, the 1st and the 2nd harmonic coefficients (i.e., C1c, C1s, C2c, and C2s), which contribute to the azimuthal sensitivity (as seen from Equation 2 below), vanish as the dip angle θ approaches zero:V({right arrow over (r)}, φ)=C0({right arrow over (r)})+C1c({right arrow over (r)})cos(φ)+C1s({right arrow over (r)})sin(φ)+C2c({right arrow over (r)})cos(2φ)+C2s({right arrow over (r)})sin 2φ)  (2)
As a result, the directional measurements defined in Equations 1a and 1b are zero, therefore improved methods for inverting tool data for resistivity anisotropy and dip angle θ for vertical wellbore sections are needed.